We study the swelling of a gel annulus attached to a rigid core when it is immersed in a solvent.For equilibrium states,the free-energy function of the gel can be converted into a strain energy function,and as a resul...We study the swelling of a gel annulus attached to a rigid core when it is immersed in a solvent.For equilibrium states,the free-energy function of the gel can be converted into a strain energy function,and as a result the gel can be treated as a compressible hyperelastic material.Asymptotic methods are used to study the inhomogeneous swelling in order to obtain the leading-order solution.Some analytical insights are then deduced.Because of the compressive hoop stress in this state,at some stage instability can occur,leading to wrinkles in the gel.An incremental deformation theory in nonlinear elasticity is used to conduct a linear bifurcation analysis for understanding such instability.More specifically,the critical loading for the onset of a wrinkled state is obtained.Detailed discussions on the behaviors of various physical quantities in this critical state are given.It is found that the critical mode number,while insensitive to the material parameters,is greatly influenced by the ratio of the inner and outer radii of the gel.Also,an interesting finding is that the critical swelling ratio is an increasing function of this geometrical parameter,which implies that a thin annulus is more likely to be unstable than a thick one.展开更多
文摘We study the swelling of a gel annulus attached to a rigid core when it is immersed in a solvent.For equilibrium states,the free-energy function of the gel can be converted into a strain energy function,and as a result the gel can be treated as a compressible hyperelastic material.Asymptotic methods are used to study the inhomogeneous swelling in order to obtain the leading-order solution.Some analytical insights are then deduced.Because of the compressive hoop stress in this state,at some stage instability can occur,leading to wrinkles in the gel.An incremental deformation theory in nonlinear elasticity is used to conduct a linear bifurcation analysis for understanding such instability.More specifically,the critical loading for the onset of a wrinkled state is obtained.Detailed discussions on the behaviors of various physical quantities in this critical state are given.It is found that the critical mode number,while insensitive to the material parameters,is greatly influenced by the ratio of the inner and outer radii of the gel.Also,an interesting finding is that the critical swelling ratio is an increasing function of this geometrical parameter,which implies that a thin annulus is more likely to be unstable than a thick one.
